Thermodynamics1: ( THIS PROBLEM IS VERY COMPLEX AND IT IS NOT JUST PUTTING THE N

Question

Thermodynamics1: ( THIS PROBLEM IS VERY COMPLEX AND IT IS NOT JUST PUTTING THE NOMBERS INTO THE EQUATION OF WORK, HEAT, AND ENTROPY)

1. A horizontal frictionless piston-and-cylinder system contains 2 moles of andideal gas and is subjected to 1.013 bar external pressure. The piston and cylinder do not conduct heat, but heat can be added to the ideal gas by a heating coil that transfers heat at 600°C. The ideal gas has an initial temperature of 300°C and enough heat is added to increase the temperature by 200°C.

Determine:
a) the work
b) heat
c) entropy of generation for this process.

Given: C_p(ideal gas)=(7/2)R

Explanation / Answer

since it is ideal gas, PV=nRT

volume of the gas => V=nRT/P ; 2 (mol) *8.314 (J/mol/K) *573 K /(101300 Pa) = 0.09406 m^3 , V(initial)

at final T=500 C = 773 K gives V= 2 (mol) *8.314 (J/mol/K) *773 K /(101300 Pa) ==> V= 0.1269 m^3, V(final)

V2-V1= 0.1269 - 0.09406

work = p(ext)(V2-V1) = 101300 Pa * 0.03284 m^3 = 3326.692 J

heat = C_p*(T2-T1) = 7/2*8.314 J/K *(773-573) K = 5819.8 J

entropy S=C_p ln(Tf/Ti) = 7/2*8.314 J/K ln(773/573) = 7/2*8.314 J/K * 0.3 = 8.73 J/K

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